Kite birdied three straight starting at the 10th. The former U.S. Open champion is still looking for the first victory of his career in his native state.
Stockton, 62, is seeking his first victory in seven years.
Hale Irwin, who leads the season-long, $1 million points race on the Champions Tour, shot a 68.
Craig Stadler, one point behind Irwin, struggled to a 74.